Question

square pqrs is transformed as shown on the graph. which rule describes the transformation? r_{0,90^{\circ}} r_{0,180^{\circ}} r_{0,270^{\circ}} r_{0,360^{\circ}}

Explanation:

Step1: Recall rotation rules

• Rotation of \(90^{\circ}\) around the origin: \((x,y)\to(-y,x)\)
• Rotation of \(180^{\circ}\) around the origin: \((x,y)\to(-x,-y)\)
• Rotation of \(270^{\circ}\) around the origin: \((x,y)\to(y, -x)\)
• Rotation of \(360^{\circ}\) around the origin: \((x,y)\to(x,y)\)

Step2: Check the transformation

Let's assume a point \(P(x,y)\) on the original square. After transformation to \(P'(x',y')\), we can see that if we take a general point \((a,b)\) on \(PQRS\), it maps to \((-a,-b)\) on \(P'Q'R'S'\). This is the rule for a \(180^{\circ}\) rotation around the origin.

Answer:

\(R_{0,180^{\circ}}\)